Refrigeration through voltage-controlled entropy change

ABSTRACT

A method for refrigeration through voltage-controlled entropy change includes applying a voltage signal to a piezoelectric material to generate strain in the piezoelectric material, generating strain in a magnetic material attached to the piezoelectric material, and generating a change in a temperature of the magnetic material in response to the strain in the magnetic material.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.13/935,176, filed on Jul. 3, 2013, which claims priority to U.S.Provisional Patent Application 61/667,472, filed on Jul. 3, 2012. Theentire contents of the above applications are hereby incorporated byreference.

BACKGROUND

According to U.S. Energy Information Administration, heating,ventilation, and cooling (HVAC) accounted for 3,856 billion kWh, or 36percent of the electricity consumed by U.S. households in 2011. Centralair-conditioning and refrigeration alone accounted for 30 percent of thetotal electricity used in homes. Improved refrigeration technology is ofmajor importance and, potentially, a big part of the solution to theenergy crisis.

There are several refrigeration technologies, such as vapor-compressionrefrigeration and magnetic refrigeration. In some implementations,magnetic refrigeration uses the magnetocaloric effect in which an activemagnetocaloric material is exposed to an external magnetic field. Theisothermal entropy change and the adiabatic temperature change are twoimportant parameters that characterize and quantify the magnetocaloriceffect. An integrated Maxwell relation determines the isothermal entropychange, ΔS. The Maxwell relation that originates from the analyticproperties of the Gibbs free energy can be expressed as follows:

$\begin{matrix}{{{\Delta\; S} = {\mu_{0}V{\int_{H_{i}}^{H_{f}}{\frac{\partial M}{\partial T}{\mathbb{d}H}}}}},} & ( {{Equ}.\mspace{14mu} 1} )\end{matrix}$

where H_(i,f) are the initial (typically zero) and final appliedmagnetic field, M is the magnetization, V is the volume of the activemagnetocaloric material, and μ₀ is the vacuum permeability. Equation 1is valid in situations where the mixed second-order derivatives of theGibbs free energy exist and the order of differentiation can beexchanged. This is the case in general, with the exception offirst-order phase transitions, where the entropy change at thetransition can be calculated with the help of the Clausius-Clapeyronequation.

SUMMARY

In one aspect, in general, a method of changing temperature throughvoltage-controlled entropy change is provided. The method includesapplying a voltage signal to a piezoelectric material to generate strainin the piezoelectric material; generating strain in a magnetic materialattached to the piezoelectric material; and generating a change in atemperature of the magnetic material in response to the strain in themagnetic material.

Implementations of the method may include one or more of the followingfeatures. Applying a voltage signal can include applying an alternatingvoltage signal. Applying the alternating voltage signal can includeapplying a first voltage to the piezoelectric material to induce a firststrain to cause a reduction in the temperature of the magnetic material,and applying a second voltage to the piezoelectric material to induce asecond strain to cause an increase in the temperature of the magneticmaterial. The method can include using the magnetic material to absorbheat from a first object after the temperature of the magnetic materialis reduced, and transferring heat from the magnetic material to a secondobject after the temperature of the magnetic material is increased.Generating a change in the temperature can include reducing thetemperature of the magnetic material. Generating a strain in a magneticmaterial can include generating a strain in a La—Sr—Mn—O compound. Thepiezoelectric material can have a grain structure, the magnetic materialcan have a grain structure, and the piezoelectric material and themagnetic material can be mixed and in contact with each other. Thepiezoelectric material can be configured as a thin film, the magneticmaterial can be configured as a thin film, and the thin film ofpiezoelectric material and the thin film of magnetic material can be incontact and form a layered structure. The piezoelectric material can beconfigured as columns that are surrounded by the magnetic material. Themagnetic material can be configured as columns that are surrounded bythe piezoelectric material.

In another aspect, in general, an apparatus for changing temperaturethrough voltage-controlled entropy change includes a piezoelectricmaterial; a magnetic material in contact with the piezoelectricmaterial; and a voltage signal generator to provide a voltage signal tothe piezoelectric material to induce strain in the piezoelectricmaterial, which induces strain in the magnetic material, which in turninduces a change in a temperature of the magnetic material.

Implementations of the apparatus may include one or more of thefollowing features. The voltage signal generator can be configured togenerate a voltage signal having a voltage level that changesperiodically. The piezoelectric material can be configured to respond tothe voltage signal by periodically stretching and relaxing, orcompressing and relaxing. The apparatus can include an actuator to causethe magnetic material to alternately move between a first position and asecond position. The actuator can cause the magnetic material to move tothe first position when the magnetic material is at a relatively lowertemperature, and cause the magnetic material to move to the secondposition when the magnetic material is at a relatively highertemperature. The magnetic material can include a ferromagnetic material.The magnetic material can include a magnetocaloric material. Themagnetic material can include a La—Sr—Mn—O compound. The piezoelectricmaterial can have a grain structure, the magnetic material can have agrain structure, and the piezoelectric material and the magneticmaterial can be mixed and in contact with each other. The piezoelectricmaterial can include a thin film of piezoelectric material, the magneticmaterial can include a thin film of magnetic material, and the thin filmof piezoelectric material and the thin film of magnetic material can bein contact and form a layered structure. The piezoelectric material caninclude columns of piezoelectric material that are surrounded by themagnetic material. The magnetic material can include columns of magneticmaterial that are surrounded by the piezoelectric material. The magneticmaterial and the piezoelectric material can be tightly bonded to eachother.

In another aspect, in general, a cooling device includes a firstmaterial that induces strain upon application of a voltage signal, inwhich a level of the strain varies in response to changes in the voltagesignal; a second material coupled to the first material, in which strainis induced in the second material when the strain is induced in thefirst material, and in which an entropy and a temperature of the secondmaterial change when the strain is induced in the second material; and avoltage signal generator to provide the voltage signal, in which thevoltage signal is configured to cause the second material to varybetween higher and lower temperatures.

Implementations of the cooling device may include one or more of thefollowing features. The first material can include a piezoelectricmaterial. The second material can include a magnetic material. Thesecond material can include a ferromagnetic material. The secondmaterial can include a magnetocaloric material. The magnetic materialcan include a La—Sr—Mn—O compound. The voltage signal generator can beconfigured to generate a voltage signal having a voltage level thatchanges periodically. The cooling device can include an actuator tocause the second material to alternately move between a first positionand a second position. The actuator can cause the second material tomove to the first position when the second material is at a relativelylower temperature, and cause the second material to move to the secondposition when the second material is at a relatively higher temperature.When the second material is at the first position, heat can flow from afirst object or region to the second material, and when the material isat the second position, heat can flow from the second material to asecond object or region. The first and second materials can have grainstructures, and the first and second materials can be mixed and incontact with each other. The first material can be configured as a firstthin film, the second material can be configured as a second thin film,and the first and second thin films can form a layered structure. Thefirst material can be configured as columns that are surrounded by thesecond material. The second material can be configured as columns thatare surrounded by the first material. The first and second materials canbe tightly bonded to each other.

The techniques described herein may have one or more of the followingadvantages. Modifying temperature of an object, such as cooling theobject, can be achieved by applying a voltage signal and withoutapplying a magnetic field. A device for changing temperature throughvoltage-controlled entropy change can be made compact and suitable forportable devices.

Other features and advantages are apparent from the followingdescription and from the claims.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a diagram of a cooling device.

FIG. 2 is a graph showing the temperature dependence of the entropy withand without an electric field.

FIGS. 3A to 3D are diagrams of suggested nanofabrication ofmagnetocaloric materials for voltage-controlled entropy change.

FIG. 4 is a flowchart of a process for cooling throughvoltage-controlled entropy change in multiferroics.

DETAILED DESCRIPTION

In the past, researchers conducting research on magnetic field-inducedcaloric effects have focused on finding optimized magnetocaloricmaterials. Based on Equation 1, one way to obtain large entropy changeis to have a large change in magnetic field. This can be achieved bymoving a magnetic material in and out of a strong magnetic fieldgenerated by a permanent magnet. The inventor recognized that Equation 1misleadingly suggests that the use of an external magnetic field ismandatory in order to achieve a sizeable isothermal entropy change. Thedescription below shows that applied magnetic fields are not necessaryto utilize the magnetocaloric effect. In addition, voltage-inducedentropy change in magnetocaloric materials has significant advantagesover conventional magnetic field-induced entropy change with thepotential to revolutionize magnetic refrigeration technology. It isbeneficial to combine the advantages of magnetocaloric andelectrocaloric materials by utilizing the magnetocaloric effect throughpure voltage control.

The following describes advantage of voltage-control over magneticfield-induced entropy change. The ordinary path towards sizableisothermal entropy change relies on applying magnetic fields to everhigher final values, H_(f), until technical saturation of themagnetization is reached. This brute-force approach has practicallimitations. When relying on the maximum achievable flux densities of1-2 Tesla of modern permanent magnets (e.g., Nd—Fe—B or Sm—Co), thefeasible adiabatic temperature changes remain below 10 K. Permanentmagnetic flux densities of the order of 4 Tesla can be generated inHalbach cylinders, but logarithmic dependence of the field on thediameter of the cylinder makes such devices very heavy. Becausepermanent magnets can generate magnetic fields in an energy efficientmanner, most of today's realizations of magnetocaloric refrigeratorsutilize a mechanism that moves the magnetocaloric material relative tothe permanent magnet in order to create a sizable change in magneticfield, ΔH=H_(f)−H_(i). The moving parts may generate noise, losses infriction, and wear-and-tear of components. The disadvantages of magneticfield-induced entropy changes can be avoided when employingvoltage-controlled entropy change in the absence of electric currents.

Referring to FIG. 1, in some implementations, near-room-temperaturerefrigeration through voltage-controlled entropy change can be achievedusing a cooling device 100 that includes a voltage signal generator 102that provides one or more voltage signals to generate an electric fieldacross piezoelectric thin films 104 a, 104 b, 104 c (collectively 104).Attached to the piezoelectric thin films 104 are ferromagnetic thinfilms 106 a, 106 b, 106 c (collectively 106). In some examples, theferromagnetic material is electrically conductive, and voltage signals108 a, 108 b, 108 c, . . . , 108 d having voltage levels V, V−ΔV, V−2ΔV,. . . , 0, respectively, can be applied to the ferromagnetic thin films106 a, 106 b, 106 c, . . . , 106 d, respectively, to generate electricfields across the piezoelectric thin films 104 a, 104 b, . . . , 104 c.In this example, a voltage difference ΔV is applied across eachpiezoelectric thin film 106 in the thickness direction. Eachpiezoelectric thin film 106 has a small thickness d, and because E=ΔV/d,a relatively small voltage difference ΔV can generate a large electricfield E across each piezoelectric thin film 104. In this configuration,the ferromagnetic thin films 106 are the active material (that changestemperature), and also function as the electric contacts for applyingthe voltage signals. Each piezoelectric thin film 104 is sandwichedbetween two electrodes, similar to a filled capacitor. The piezoelectricthin films 104 can be made of, e.g., PbMg_(1/3)Nb_(2/3)O₃—PbTiO₃(001)(PMN-PT), and the ferromagnetic thin films 106 can be made of, e.g.,La_(0.7)Sr_(0.3)MnO₃ (referred to as LSMO or La—Sr—Mn—O compound).

In some implementations, a voltage signal V1 is applied to the topferromagnetic layer 106 a, and a voltage signal V2 is applied to thebottom ferromagnetic layer 106 d. The voltage difference V1−V2=ΔVgenerates an electric field between the top and bottom ferromagneticlayers 106, in which the electric field is applied across thepiezoelectric thin films 104. In this example, the voltage signalgenerator 102 only needs to output two voltage signals having differentvoltage levels.

The voltage signal 108 can have, e.g., a sinusoidal waveform or asawtooth waveform. The voltage signal 108 can have an alternatingwaveform having a voltage level that varies periodically. When thevoltage signal 108 is applied to the thin films, strain is induced inthe piezoelectric thin films 104. Because the ferromagnetic thin films106 are attached to the piezoelectric thin films 104, the strain in thepiezoelectric thin films 104 causes strain to be induced in theferromagnetic thin films 106. When strain is induced in theferromagnetic thin films 106, the magnetization of the ferromagneticmaterial changes, the entropy of the ferromagnetic thin films 106changes, and the temperature of the ferromagnetic thin films 106changes.

By controlling the voltage signal 108, the temperature of theferromagnetic thin films 106 can be made to increase or decrease. Forexample, suppose the voltage signal 108 alternates between a highpositive voltage level and zero. When the high voltage level is appliedto the piezoelectric thin films 104, strain is induced in thepiezoelectric thin films 104 and the ferromagnetic thin films 106,causing magnetization of the ferromagnetic thin films 106 to decrease(or increase depending on the bias strain the film has at zero voltage)from the original state (the state when no voltage is applied), therebycausing the entropy to increase in an isothermal situation and, in anadiabatic situation suitable for the refrigeration application,temperature to decrease. When the zero voltage level is applied to thepiezoelectric thin films 104, strain is removed from in thepiezoelectric thin films 104 and the ferromagnetic thin films 106,causing magnetization of the ferromagnetic thin films 106 to increaseand return to the original state, thereby causing the entropy todecrease and temperature to increase.

For example, each of the LSMO thin films can have a thickness in theorder of a few nanometers to tens of nanometers, e.g., 20 nm. Anadvantage of using LSMO thin films instead of LSMO bulk material is thatstrain can be induced in a large portion (e.g., the entire portion) ofthe LSMO thin film, which increases the magnetocaloric effect, resultingin a larger temperature change. If LSMO bulk material is used, strain isinduced only near the surface of the LSMO material that is in contactwith the piezoelectric material so that the magnetocaloric effect issmaller (for a given amount of LSMO material).

The following describes the mechanism for realization ofvoltage-activated entropy change using the magnetocaloric effect. Insome implementations, piezoelectrically-induced strain can be used tocontrol anisotropy and critical temperature of magnetic materials. Forexample, piezoelectrically-induced strain can be used to substantiallychange the magnetic anisotropy in iron (Fe) thin films or used tocontrol the exchange-bias field in an exchange-bias magneticheterostructure. Similarly, strain originating from stress can beinduced via the inverse piezoelectric effect. The strain, when carriedover into an adjacent magnetic thin film, can substantially change themagnetic Curie temperature, T_(C) of the magnetic material. An externalcontrol parameter such as tensile or compressive strain can tune thedegree of magnetic order in a magnetically long-range ordered system.Decrease (increase) in long-range magnetic order can be accompanied by asignificant increase (decrease) in entropy. The transition from aparamagnetic into a long-range ordered magnetic state is accompanied bysizeable entropy reduction.

For example, a compressively strained La_(0.7)Sr_(0.3)MnO₃ (LSMO) filmof 16 nm thickness on LaAlO₃ (001) changes the Curie temperature of theformer from 365 K (unstrained) to 270 K (strained through latticemismatch). Voltage-controlled epitaxial strain in LSMO can be achievedwhen exploiting the inverse piezoelectric effect ofPbMg_(1/3)Nb_(2/3)O₃—PbTiO₃(001) (PMN-PT) substrates. When thetemperature of a permanent magnet increases above a certain point,referred to as the Curie temperature, the permanent magnetism changes toparamagnetism. For a given temperature, the magnetization of the LSMOfilm increases when an electric field is applied to the compressivelystrained La_(0.7)Sr_(0.3)MnO₃ (LSMO) film on LaAlO₃ (001). In addition,when an electric field is applied to the compressively strainedLa_(0.7)Sr_(0.3)MnO₃ (LSMO) film on LaAlO₃ (001), the Curie temperature(or critical temperature) in the LSMO film tends to increase. Variousparameters allow fine-tuning of the critical temperature at zero appliedvoltage. The tuning parameters include the Sr concentration of the LSMOcompound, the film thickness, and the initial strain in zero-appliedelectric field.

Changes of the critical temperature, T_(C), of ferromagnetic thin filmssuch as the complex oxide LSMO can be achieved by pure voltage-control,in which the inverse piezoelectric effect is used in order to strain theLSMO film in an electrically controlled manner. Large magnetoelectricsusceptibilities can be achieved, e.g., in complex oxides, when usingthe electric field effect. For example, sizable electric modulation ofmagnetization in a BaTiO₃/LSMO heterostructure can be achieved. Theelectric field-controlled metal-insulator transition in the LSMO filmproduces a large magnetoelectric effect that can be used in the same wayas the strain-induced change in magnetization.

The following describes thermodynamic consequences of largemagnetoelectric effects and their impact on voltage-controlledisothermal entropy change. Theoretical basis for the voltage-controlledentropy change is described below. The differential form of theHelmholtz free energy, F, of a magnetic system, can be represented asfollows:dF=−SdT+μ ₀ VHdM.  (Equ. 2)

When the applied magnetic field is zero, the variable H in Equation 2can be considered to be the internal magnetic field, which depends ontemperature T and the equilibrium magnetization M. The magnetization inturn is a function of a control parameter, which in this case is theelectric field E. Therefore, the equation of state can be written asH=H(T,M(E))  (Equ. 3)From Equation 2, we derive a Maxwell relation by identifying the mixedsecond-order derivatives of the Helmholtz free energy:

$\begin{matrix}{( \frac{\partial S}{\partial M} )_{T} = {{- \mu_{0}}{{V( \frac{\partial H}{\partial T} )}_{M}.}}} & ( {{Equ}.\mspace{14mu} 4} )\end{matrix}$Integration of Equation 4 provides the expression:

$\begin{matrix}{{{\Delta\; S} = {{- \mu_{0}}V{\int_{M_{i}}^{M_{f}}{( \frac{\partial H}{\partial T} )_{M}\ {\mathbb{d}M}}}}},} & ( {{Equ}.\mspace{14mu} 5} )\end{matrix}$for the isothermal entropy change. Note that Equation 5 differs fromEquation 1, which is derived from a different Maxwell relationoriginating from the Gibbs free energy.

Using thermodynamic identities,

${{( \frac{\partial H}{\partial T} )_{M}( \frac{\partial M}{\partial H} )_{T}( \frac{\partial T}{\partial M} )_{H}} = {- 1}},$we get

${( \frac{\partial H}{\partial T} )_{M} = {{- \frac{1}{x}}( \frac{\partial M}{\partial T} )_{H}}},$which leads after substitution into Equation 5 a formula for theisothermal entropy change:

$\begin{matrix}{{{\Delta\; S} = {\int_{M_{i}}^{M_{f}}{\frac{\mu_{0}V}{\chi}( \frac{\partial M}{\partial T} )_{H}\ {\mathbb{d}M}}}},} & ( {{Equ}.\mspace{14mu} 6} )\end{matrix}$where

$\chi = ( \frac{\partial M}{\partial H} )_{T}$is the magnetic susceptibility. From the fact that M depends on thecontrol parameter, E, we substitute

${dM} = {( \frac{\partial M}{\partial E} )_{T}{dE}}$to obtain

$\begin{matrix}{{\Delta\; S} = {\int_{E_{i} = 0}^{E_{f}}{\frac{\mu_{0}V}{\chi}( \frac{\partial M}{\partial T} )_{H}( \frac{\partial M}{\partial E} )_{T}\ {{\mathbb{d}E}.}}}} & ( {{Equ}.\mspace{14mu} 7} )\end{matrix}$

The following describes numerical estimates for voltage-controlledentropy change in a heterostructure that includes a piezoelectricmaterial PMN-PT and a magnetocaloric material LSMO. The values of theparameters can be estimates or values based on experiment data. Tofurther explore the consequences of Equation 7, we consider the Landauexpression F=F₀(T)+½AM²+¼BM⁴−μ₀VHM. Here, A=a₀(T−T_(C)(E)), a₀ and B arepositive constants, and F₀ is a regular temperature-dependentbackground. The Landau expression allows specifying M and x in terms ofthe expansion coefficients. This yields the entropy change forT≦T_(C)(0)

$\begin{matrix}{{\Delta\; S} = {{- \frac{a_{0}^{2}}{2\; B}}( {{T_{C}(E)} - {T_{C}(0)}} )}} & ( {{Equ}.\mspace{14mu} 8} )\end{matrix}$One can replace the parameters of the Landau expansion using

$\frac{a_{0}}{B} = {{\frac{M^{2}( {T = 0} )}{T_{c}}\mspace{14mu}{and}\mspace{14mu}\frac{\mu_{0}V}{\chi( {2\; T_{c}} )}} = {a_{0}T_{c}}}$which yields

$\begin{matrix}{{\Delta\; S} = {{- \frac{\mu_{0}{{VM}^{2}( {T = 0} )}}{2{\chi( {2\; T_{c}} )}T_{c}^{2}}}{( {{T_{C}(E)} - {T_{C}(0)}} ).}}} & ( {{Equ}.\mspace{14mu} 9} )\end{matrix}$

For example, using a density value for LSMO of ρ=6600 kg/m³, wecalculate a mass-specific isothermal entropy change which can now beused for comparison with current state-of-the-art magneticfield-induced, specific entropy changes. For example, the saturationmagnetization of a pulsed laser deposited LSMO film of 30% Srconcentration can be M(T=0)≈0.45 MA/m. We use the mean-field expression,

$\begin{matrix}{{\frac{\mu_{0}{M(0)}}{\chi(T)} = {\frac{3\; k_{B}T_{C}}{g\;{\mu_{B}( {S + 1} )}}( {\frac{T}{T_{C}} - 1} )}},} & ( {{Equ}.\mspace{14mu} 10} )\end{matrix}$which for T=2T_(C) yields

${{\chi( {2\; T_{c}} )} = \frac{\mu_{0}g\;{\mu_{B}( {S + 1} )}{M(0)}}{3\; k_{B}T_{C}}},$where S≈3.5. Using further a Landé g-factor of g≈2 in accordance withRef.(^(i)), T_(C)(E=0)=279K and ΔT_(C)=T_(C)(E=7 kV/cm)−T_(C)(0)=19 K,we estimate the value of the specific entropy change, which yields

${\Delta\;{S/m}} = {{- 1.15}{\frac{J}{kgK}.}}$

Note that S(T, E) and, therefore, Equation 8 can be directly calculatedfrom the Landau free energy according to

$S = {- {( \frac{\partial F}{\partial T} )_{M}.}}$This yields

$\begin{matrix}{{S( {T,E} )} = {{- ( \frac{\partial F}{\partial T} )_{M}} = {{{{- \frac{1}{2}}\frac{\partial A}{\partial T}M^{2}} + S_{0}} = \{ \begin{matrix}{{{- \frac{a_{0}^{2}}{2\; B}}( {{T_{C}(E)} - T} )} + S_{0}} & {{{for}\mspace{14mu} T} < {T_{C}(E)}} \\S_{0} & {{{for}\mspace{14mu} T} > {T_{C}(E)}}\end{matrix} }}} & ( {{Equ}.\mspace{14mu} 11} )\end{matrix}$

Equations 7 and 11 are both useful. Equation 7 is free fromapproximations. Also, χ and M(T,E) can be measured while the Landau freeenergy is a crude approximation of the underlying thermodynamicpotential F and may not be experimentally accessible.

Alternatively, we estimate the mass-specific isothermal entropy changeat T=280 K from the magnetoelectric susceptibility,

${\alpha = {\mu_{0}\frac{\partial M}{\partial E}}},$of PMN-PT/LSMO. The numerical value of a is determined from the dataadapted from C. Thiele, K. Dörr, O. Bilani, J. Rödel, and L. Schultz,Phys. Rev. B 75, 054408 (2007). For E=0 and 7 kV/cm the magnetizationdata can be described by the functions

${M( {T,{E = 0}} )} = {10^{4}\sqrt{( {{2.63 \times 10^{3}} - {9.27\;{T/K}}} )}\frac{A}{m}\mspace{20mu}{and}}$${M( {T,{E = {7\;{{kV}/{cm}}}}} )} = {10^{4}\sqrt{( {{3.24 \times 10^{3}} - {10.89{T/K}}} )}\frac{A}{m}}$which yields

${{\alpha( {T = {280\mspace{11mu} K}} )} \approx {{\mu_{0}( {{M( {{T = {280\mspace{11mu} K}},{E = {7\mspace{14mu}{kV}\text{/}{cm}}}} )} - {M( {{T = {280\mspace{11mu} K}},{E = 0}} )}} )}/( {7.0 \times 10^{5}\mspace{11mu} V\text{/}m} )}} = {2.41 \times 10^{- 7}{\frac{s}{m}.}}$We use this value of magnetoelectric susceptibility for furtherestimates and neglect the details of the temperature dependence of α. Weuse a rough estimate for

${M(0)} = {0.51 \times 10^{6}\frac{A}{m}}$for LSMO by extrapolating M (T, E=0) towards T=0. The extrapolation ofthe Landau expression overestimates the magnetization at T=0 which, inturn, gives rise to an underestimation of the isothermal entropy change.We obtain

$( \frac{\partial M}{\partial T} )_{{T = {280\mspace{11mu} K}},{E = 0}} = {{- 8.53}\frac{kA}{mK}}$from the M (T, E=0) function. We assume a linear dependence of T_(C) onthe applied electric field which reads T_(C)(E)=2.43×10⁻⁵ E Km/V+280 K.Using Equation 10 to quantify χ(T, T_(C)(E)), we estimate themass-specific isothermal entropy change from

$\begin{matrix}{{\Delta\;{S/m}} = {\int_{0}^{E}{\frac{\alpha}{{\chi( {T,T_{C}} )}\rho}( \frac{\partial M}{\partial T} )_{H}\ {{\mathbb{d}E}.}}}} & ( {{Equ}.\mspace{14mu} 12} )\end{matrix}$It yields

${\Delta\;{S/m}} = {{- 1.43}\frac{J}{kgK}}$in good agreement with the alternative approach based on Equation 9 andoutlined above. The remaining difference in the numerical values of thespecific isothermal entropy changes originates from differences in theassumptions and approximations. Equation 12 shows that entropy changecan be achieved without applying a magnetic field.

The following describes refrigerant capacity and implications forrefrigeration applications. The voltage-induced entropy change estimatedabove is of respectable magnitude when compared, e.g., with the bulkgiant magnetocaloric material Gd₅Si₂Ge₂, which represents a benchmarkfor magnetocaloric materials. Gd₅Si₂Ge₂ has an isothermal entropy changeof approximately 4 J/kgK when an external magnetic field is ramped fromzero to 1 Tesla. Although this value is still approximately twice theentropy change we estimate for the voltage-controlled effect inPMN-PT/LSMO, it is important to realize that for virtually allmagnetocaloric materials and Gd₅Si₂Ge₂ in particular, the isothermalentropy change strongly peaks at a given temperature, T_(max), anddecreases for both higher and lower temperatures. This limits therefrigerant capacity (RC), which is the figure-of-merit of arefrigerator. The refrigerant capacity can be calculated from thetemperature-dependence of the isothermal entropy change according to

RC = ∫_(T_(max) − Δ T/2)^(T_(max) + Δ T/2)Δ S𝕕T.Here ΔT is the width of ΔS(T) at half-maximum. Therefore, for the narrowGaussian S vs. T behavior, the refrigerant capacity is limited despitepotentially large values of S at the maximum of S vs. T.

In the case of voltage-controlled entropy change, S vs. T will remainvirtually constant for all T<T_(C)(0) at the value given by Equation 9.The absolute value of the entropy change decreases linearly to zero forT>T_(C)(0) and remains zero for T≧T_(C)(E).

Referring to FIG. 2, a graph 120 shows the temperature dependencies ofS(T, E=0) (circles, left axis), S(T, E=E_(f)>0) (squares, left axis) andΔ(S(T, E=E_(f)>0)−S(T, E=0)) (right axis) as given by Equation 11. Datapoints 122 (circles) represent the entropy S relative to a referencevalue S₀ for various temperatures when no electric field is applied(E=0). Data points 124 (squares) represent the entropy S relative to thereference value S₀ for various temperatures when an electric field isapplied (E=E_(f)>0).

Dashed line 128 indicates the critical temperature T_(C)(0) of theferromagnetic film in electric field E=0. Dashed line 128 indicates thecritical temperature T_(C)(E=E_(f)) of the ferromagnetic film inelectric field E=E_(f). The line 126 shows ΔS, which is the differencebetween the entropy value when voltage is applied, and the entropy valuewhen a voltage is applied. The line 126 (right axis) shows thetemperature dependence of the isothermal entropy change. The line 126indicates that a significant difference in entropy ΔS exists (|ΔS|≈0.19)for a wide range of temperature values, e.g., from less than 200K toabout 278K. This indicates that the cooling device 100 can be used forcooling for a wide range of temperatures. The absolute value of theentropy difference |ΔS| decreases from about 0.19 to 0 when thetemperature increases from about 278K to about 298K. This indicates thatthe cooling device 100 is useful for room temperature coolingapplications.

The temperature independence of S vs. T for the temperatures T<T_(C)(0)largely increases the refrigerant capacity to values potentially muchhigher than those reported in the literature. The emphasis here is toachieve sizeable entropy change in the absence of applied magneticfields. Pure voltage-controlled entropy change broadens the range ofpotential applications when compact cooling solutions with little to nomechanical vibrations are required.

The following describes realization of multiferroic materials forvoltage-controlled entropy change. The bilayer system PMN-PT/LSMO shownin FIG. 1 can be considered a generic and prototypical building block ofa two-phase multiferroic material, allowing for voltage-controlledentropy change. In general, composite materials combining apiezoelectric material with a magnetic material of sizeablemagnetoelastic response or other sources of large magnetoelectricresponse in multiferroic systems near room temperature are capable offunctioning as a potential candidate for voltage-controlled entropychange.

Another candidate of a magnetoelectric composite for magnetocaloricapplications is a laminate composite of piezoelectric AlN and amorphousFeCoSiB which can be fabricated by sputtering methodology and has a highmagnetoelectric effect at room temperature. Operation of the laminate inalternating current (AC) mode at resonance frequency and in the presenceof a small biasing magnetic field (order of the Earth's magnetic field)gives rise to α≈1.4 10⁻⁷ s/m, which may prove suitable as an alternativeto the complex oxide composites analyzed here in more detail.

The M-type hexaferrite SrCo₂Ti₂Fe₈O₁₉ shows a promising largemagnetoelectric effect at room temperature, which is about 50 timeshigher than the maximum magnetoelectric susceptibility α≈4 10⁻¹² s/m ofthe archetypical magnetoelectric chromia. Although the bulkmagnetoelectric susceptibility is orders of magnitude below themagnetoelectric response of LSMO and FeCoSiB composites, the bulkmagnetoelectric multiferroics may be produced at a lower cost and can bealternatives to the composite materials that include nanolayers of LSMO.

Referring to FIGS. 3A to 3D, for applications in magnetocaloricrefrigeration, macroscopic amounts of active material are used. Severalfabrication strategies can be used. Referring to FIG. 3A, in someexamples, a mixture 130 that includes grains of piezoelectric material132 (e.g., PMN-PT) and grains of magnetic material 134 havingmagnetoelastic properties (e.g., LSMO) can be used. The grains ofpiezoelectric material 132 and grains of magnetic material 134 can bebonded together using an adhesive material.

Referring to FIG. 3B, in some examples, a thin film heterostructure 140can be used. The thin film heterostructure 140 includes a large numberof repetitions of a bilayer building block, in which each building blockincludes a layer of piezoelectric material 142 and a layer of magneticmaterial 144.

Referring to FIG. 3C, in some examples, a columnar structure ofpiezoelectric material in a magnetic matrix can be used. For example, anordered nanostructured arrangement 150 such as nanopillars of magneticmaterial 152 in a piezoelectric matrix 154 can be used.

Referring to FIG. 3D, in some examples, a columnar structure of magneticmaterial in a piezoelectric matrix can be used. For example, an orderednanostructured arrangement 160 such as nanopillars of piezoelectricmaterial 162 in a matrix of magnetic material 164 can be used. Here, theoptimum structural choice will be affected by additional constraintssuch as optimized thermal conductivity.

The concept of voltage-controlled entropy change in magnetocaloricmaterials for magnetic refrigeration applications has been describedabove. One of the key features of this approach is that themagnetocaloric effect is utilized without applying an external magneticfield. We estimate a specific isothermal voltage-controlled entropychange for the bilayer heterostructure PMN-PT/LSMO is larger than 1J/kgK and serves as proof of principle for voltage-controlled magneticrefrigeration near room temperature.

Referring to FIG. 4, a process 170 for cooling an object usingvoltage-controlled entropy change in multiferroics is provided. Forexample, the process 170 can be implemented using the cooling device 100of FIG. 1. The process 170 includes applying a voltage signal to apiezoelectric material to generate strain in the piezoelectric material(172). The applied voltage increases strain in a magnetic materialattached to the piezoelectric material (174). The temperature of themagnetic material is decreased in adiabatic response to the increasedstrain in the magnetic material (176). Heat is transferred from anobject to be cooled to the cooled magnetic material (178). The voltagesignal is modified to reduce the strain in the piezoelectric material,resulting in a decrease in the strain in the magnetic material (180).The temperature of the magnetic material is increased in response to thedecrease of the strain in the magnetic material (182). Heat isdissipated from the heated magnetic material (184).

The foregoing description is intended to illustrate and not to limit thescope of the invention, which is defined by the scope of the appendedclaims. Other embodiments are within the scope of the following claims.For example, the thicknesses and the materials used for thepiezoelectric thin films and the magnetic thin films can be differentfrom those described above. The critical temperatures and the amount ofentropy change in the materials can be different from those describedabove.

Instead of using a two-phase composite material having distinctpiezoelectric material component and ferromagnetic material component, amagnetoelectrically active material in bulk compound form having a highmagnetoelectric susceptibility can also be used. For example, the bulkcompound may have piezoelectric grains mixed with ferromagnetic grains.The magnetoelectrically active material in bulk compound form can bemade at a lower cost (compared to using the piezoelectric thin films andferromagnetic thin films). When a voltage difference is applied toelectrodes across the magnetoelectrically active material, an electricfield is generated across the magnetoelectrically active material,causing the magnetization of the magnetoelectrically active material tochange, and in an adiabatic situation causing the temperature of themagnetoelectrically active material to change.

In FIG. 1, when the voltage signal is applied to generate strain, themagnetization in the magnetic material changes. In an isothermalsituation, the entropy changes in response to the change inmagnetization without a change in temperature, whereas in an adiabaticsituation, the temperature changes without a change in entropy. It isalso possible to have a combination of some entropy change and sometemperature change in response to the change in magnetization. Thus, acooling device made using the techniques described above can have achange in magnetization accompanied by a change in temperature without achange in entropy, or have a change in magnetization accompanied by botha change in temperature and a change in entropy.

In FIG. 1, as the voltage signal is applied to the combination ofmagnetic and piezoelectric thin films, the temperature of the thin filmsalternate between high to low levels. In some implementations, anactuator is used to cause the thin films to alternately move between afirst position and a second position. In the first position, the thinfilms are in contact with, or in the vicinity of, a first object to becooled and absorbs heat from the first object. When the thin films arein the second position, the thin films are positioned away from thefirst object, and are in contact with, or in the vicinity of, a secondobject and dissipates heat to the second object. For example, the firstobject can be an electronic component that needs to be cooled, and thesecond object can be a heat sink or heat pipe. For example, the firstobject can be a first heat pump that transfers heat from a coolingchamber of a refrigerator to the thin films at the first position. Thesecond object can be a second heat pump that transfers heat from thethin films in the second position to a heat dissipating apparatus, suchas cooling fins. The movement of the thin films between the first andsecond positions is synchronized with the variation of voltage levelsapplied to the thin films. A controller may be used to control theactuator and the voltage signal generator so that they operatesynchronously.

What is claimed is:
 1. A cooling device, comprising: a first materialthat induces strain upon application of a voltage signal, in which alevel of the strain varies in response to changes in the voltage signal;a second material coupled to the first material, in which strain isinduced in the second material when the strain is induced in the firstmaterial, and in which an entropy and a temperature of the secondmaterial change when the strain is induced in the second material; and avoltage signal generator to provide the voltage signal, in which thevoltage signal is configured to cause the second material to varybetween higher and lower temperatures.
 2. The cooling device of claim 1in which the first material comprises a piezoelectric material.
 3. Thecooling device of claim 1 in which the second material comprises amagnetic material.
 4. The cooling device of claim 3 in which the secondmaterial comprises a ferromagnetic material.
 5. The cooling device ofclaim 3 in which the second material comprises a magnetocaloricmaterial.
 6. The cooling device of claim 3 in which the magneticmaterial comprises a La—Sr—Mn—O compound.
 7. The cooling device of claim1 in which the voltage signal generator is configured to generate avoltage signal having a voltage level that changes periodically.
 8. Thecooling device of claim 1, comprising an actuator to cause the secondmaterial to alternately move between a first position and a secondposition.
 9. The cooling device of claim 8 in which when the secondmaterial is at the first position, heat flows from a first object orregion to the second material, and when the second material is at thesecond position, heat flows from the second material to a second objector region.
 10. The cooling device of claim 1 in which the first andsecond materials have grain structures, and the first and secondmaterials are mixed and in contact with each other.
 11. The coolingdevice of claim 1 in which the first material is configured as a firstthin film, the second material is configured as a second thin film, andthe first and second thin films form a layered structure.
 12. Thecooling device of claim 1 in which the first material is configured ascolumns that are surrounded by the second material.
 13. The coolingdevice of claim 1 in which the second material is configured as columnsthat are surrounded by the first material.
 14. The cooling device ofclaim 1 in which the first and second materials are tightly bonded toeach other.
 15. A method of cooling a device, the method comprising:applying a voltage signal to a first material to induce strain in thefirst material, in which the first material is selected to have aproperty such that the first material induces strain upon application ofthe voltage signal, and a level of the strain varies in response tochanges in the voltage signal; inducing strain in a second material thatis coupled to the first material; and generating a change in an entropyand a temperature of the second material in response to the strain inthe second material.
 16. The method of claim 15 in which applying thevoltage signal to the first material comprises applying the voltagesignal to a piezoelectric material.
 17. The method of claim 15 in whichinducing the strain in the second material comprises inducing the strainin a magnetic material.
 18. The method of claim 17 in which inducing thestrain in the second material comprises inducing the strain in aferromagnetic material.
 19. The method of claim 17 in which inducing thestrain in the second material comprises inducing the strain in amagnetocaloric material.
 20. The method of claim 17 in which inducingthe strain in the second material comprises inducing the strain in aLa—Sr—Mn—O compound.
 21. The method of claim 15 in which applying thevoltage signal comprises applying an alternating voltage signal having avoltage level that changes periodically.
 22. The method of claim 21 inwhich applying the alternating voltage signal comprises applying a firstvoltage to the first material to induce a first strain to cause areduction in the temperature of the second material, and applying asecond voltage to the first material to induce a second strain to causean increase in the temperature of the second material.
 23. The method ofclaim 15, comprising alternately moving the second material between afirst position and a second position.
 24. The method of claim 23,comprising flowing heat from a first object or region to the secondmaterial when the second material is at the first position, and flowingheat from the second material to a second object or region when thesecond material is at the second position.
 25. The method of claim 15 inwhich the first and second materials have grain structures, and thefirst and second materials are mixed and in contact with each other. 26.The method of claim 15 in which the first material is configured as afirst thin film, the second material is configured as a second thinfilm, and the first and second thin films form a layered structure. 27.The method of claim 15 in which the first material is configured ascolumns that are surrounded by the second material.
 28. The method ofclaim 15 in which the second material is configured as columns that aresurrounded by the first material.
 29. The method of claim 15 in whichthe first and second materials are tightly bonded to each other.